Question: Rewrite as a simplified fraction. ${0.8\overline{52} = {?}}$
Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}1000x &= 852.5252...\\ 10x &= 8.5252...\end{align*}}$ Subtracting the two equations, we have: ${990x = 844}$ ${x = \dfrac{844}{990}} $ ${x = \dfrac{422}{495}} $